4.1.8 Conservation of Energy

Principle of Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transferred from one form to another. In a closed system (where no energy enters or leaves), the total energy remains constant.

Mathematically:

$$\text{Total energy in} = \text{Total energy out}$$

This principle is useful for solving problems involving gravitational potential energy $(\Delta E_p)$ and kinetic energy $( E_k )$.

Formulas for Energy:

1. Gravitational Potential Energy (GPE):

$$\Delta E_p = m \times g \times \Delta h$$

Where:

• m = mass of the object ($kg$)
• g = gravitational field strength (9.81 m/s²)
• $\Delta h$ = change in height ($m$)

2. Kinetic Energy ($KE$):

$$E_k = \frac{1}{2} m v^2$$

Where:

• $m$ = mass of the object ($kg$)
• $v$ = velocity of the object ($m/s$)

Imagine a ball being thrown into the air. Initially, the kinetic energy given by the thrower propels the ball upward. As it rises, kinetic energy is gradually transferred to gravitational potential energy as the ball gains height. Eventually, at the ball's highest point, all kinetic energy is converted into potential energy, momentarily making its velocity zero.

Then, as the ball starts to fall back down, gravitational potential energy is converted back into kinetic energy. When it reaches the ground, most of this energy will have been converted back to kinetic energy (ignoring air resistance).